Harmonic Analysis Method for Nonlinear Evolution Equations, I PDF Download

Author: Baoxiang Wang
Publisher: World Scientific
ISBN: 9814458392
Category : Mathematics
Languages : en
Pages : 300

View

Book Description
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein–Gordon equations, KdV equations as well as Navier–Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods. This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students. Contents:Fourier Multiplier, Function Spaces Xsp,qNavier–Stokes EquationStrichartz Estimates for Linear Dispersive EquationsLocal and Global Wellposedness for Nonlinear Dispersive EquationsThe Low Regularity Theory for the Nonlinear Dispersive EquationsFrequency-Uniform Decomposition TechniquesConservations, Morawetz' Estimates of Nonlinear Schrödinger EquationsBoltzmann Equation without Angular Cutoff Readership: Graduate students and researchers interested in analysis and PDE. Keywords:Nonlinear Dispersive Equation;Harmonic Analysis MethodKey Features:From PDE point of view, this book gives a self-contained introduction to the theory of function spaces including Besov, modulation and Triebel–Lizorkin spacesThe main topics are concentrated in four kinds of important equations, nonlinear Schrödinger, Navier–Stokes, KdV and Boltzmann equationsThis monograph is a unique treatment of the frequency-uniform localization techniques for nonlinear evolution equationsReviews: "The book under review is well and clearly written and pleasant to read. It is aimed at advanced graduate students; hence, familiarity with basic topics in measure theory, real analysis, complex analysis, functional analysis, etc., is assumed on the part of the reader. Those mathematicians who wish to learn harmonic analysis methods used in PDEs, and who wish to enter into this active area of research, will surely find this book interesting. The book also contains a reasonably large bibliography." Mathematical Reviews

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

View

Book Description

Author: J. Kral
Publisher: Springer Science & Business Media
ISBN: 1461344255
Category : Mathematics
Languages : en
Pages : 138

View

Book Description
Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.

Author: Elena Cordero
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311053245X
Category : Mathematics
Languages : en
Pages : 458

View

Book Description
This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.

Author: Willy Dörfler
Publisher: Springer Nature
ISBN: 3030471748
Category : Mathematics
Languages : en
Pages : 330

View

Book Description
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

Author: Reinhard Racke
Publisher: Birkhäuser
ISBN: 3319218735
Category : Mathematics
Languages : en
Pages : 306

View

Book Description
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.

Author: Árpád Bényi
Publisher: Springer Nature
ISBN: 1071603329
Category : Mathematics
Languages : en
Pages : 177

View

Book Description
This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

Author: Elena Prestini
Publisher: Birkhäuser
ISBN: 1489979891
Category : Mathematics
Languages : en
Pages : 356

View

Book Description
A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University “The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded.” — Society for Industrial and Applied Mathematics “This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier’s expression) to ‘the public good and the explanation of natural phenomena.’ ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics.” — Mathematical Association of America Reviews

Author: Songmu Zheng
Publisher: CRC Press
ISBN: 1135436479
Category : Mathematics
Languages : en
Pages : 302

View

Book Description
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator methods, the monotone iterative method and invariant regions, the global existence and uniqueness theory for small initial data, and the asymptotic behavior of solutions and global attractors. Many of the results are published in book form for the first time. Bibliographic comments in each chapter provide the reader with references and further reading materials to enable further research and study.

Author: Ali Soofastaei
Publisher: BoD – Books on Demand
ISBN: 1803569530
Category : Computers
Languages : en
Pages : 342

View

Book Description
Numerical simulation is a powerful tool used in various fields of science and engineering to model complex systems and predict their behavior. It involves developing mathematical models that describe the behavior of a system and using computer algorithms to solve these models numerically. By doing so, researchers and engineers can study the behavior of a system in detail, which may only be possible with analytical methods. Numerical simulation has many advantages over traditional analytical methods. It allows researchers and engineers to study complex systems’ behavior in detail and predict their behavior in different scenarios. It also allows for the optimization of systems and the identification of design flaws before they are built. However, numerical simulation has its limitations. It requires significant computational resources, and the accuracy of the results depends on the quality of the mathematical models and the discretization methods used. Nevertheless, numerical simulation remains a valuable tool in many fields and its importance is likely to grow as computational resources become more powerful and widely available. Numerical simulation is widely used in physics, engineering, computer science, and mathematics. In physics, for example, numerical simulation is used to study the behavior of complex systems such as weather patterns, fluid dynamics, and particle interactions. In engineering, it is used to design and optimize systems such as aircraft, cars, and buildings. In computer science, numerical simulation models and optimization algorithms and data structures. In mathematics, it is used to study complex mathematical models and to solve complex equations. This book familiarizes readers with the practical application of the numerical simulation technique to solve complex analytical problems in different industries and sciences.